Cheat Sheet 2 Math 141 - Department of Mathematics

Cheat Sheet 2

Let A = accumulated balance after Y years P = starting principal AP R = annual percentage rate (as a decimal) n = number of compounding periods per year Y = number of years (may be a fraction) P M T = regular payment (deposit) amount a = inflation rate (a decimal) i = interest rate (a decimal)

Math 141

Simple Interest Formula: Compound Interest Formula:

Annual Percentage Yield: APY

Continuous Compounding Formula:

A = P (1 + AP R Y )

A

=

P (1

+

AP n

R

)nY

AP Y

=

(1

+

AP n

R

)n

-

1

A = P eAP RY

Savings Plan Formula: Total and Annual Return:

Current Yield of a Bond:

A

=

PMT

[(1+

AP R n

)nY

-1]

AP R

n

totalreturn

=

A-P P

annualreturn =

A P

(1/Y ) - 1

current

yield

=

annual interest payment current price of bond

Loan Payment Formula:

AP R

PMT = P

n

( ) 1-

1+

AP n

R

(-nY )

The CPI Formula

= CP IX

CP IY

priceX priceY

The Present Value of a principal P, Y years into the future, r=APR, a=annual inflation:

A

=

P

[

1+r 1+a

]Y

Real Growth g:

g

=

r-a 1+a

Real Growth over Y years:

g(Y )

=

[1 +

r-a 1+a

]Y

-1

The Tax Table: single

10%

1 - 9,275

15% 9,276 - 37,650

25% 37,651 - 91,150

28% 91,151 - 190,150

33% 190,151 - 413,350

35% 413,351 - 415,050

39.6%

415,051 +

m(joint) 1-18,550 18,551 - 75,300 75,301 - 151,900 151,901 - 231,450 231,451 - 413,350 413,351 - 466,950 466,951 +

m(separate) 1 - 9,275

9,276 - 37,650 37,651 - 75,950 75,951 - 115 725 115,726 - 206,675 206,676 - 233,475

233,476 +

head household 1-13,250

13,251 - 50,400 50,401 - 130,150 130,151 - 210,800 210,801 - 413,350 413,351 - 441,000

441,001 +

The mean of x1, x2, ...xn is

?

=

. x1+x2+...+xn n

The variance s2 of x1, x2, ...xn is

s = . 2 (x1-?)2+(x2-?)2+...+(xn-?)2 n-1

The standard deviation s is the square root of the variance s2.

Quartiles of Normal Distributions: Q1 = mean - .67 s Q3 = mean + .67 s

The 68 - 95 - 99.7 Rule for normal distributions: 68% of the observations fall within 1 standard deviation of the mean. 95% of the observations fall within 2 standard deviations of the mean. 99.7% of the observations fall within 3 standard deviations of the mean.

Given data (x1, y1), (x2, y2), ... (xn, yn), with means ?x, ?y and standard deviations sx, sy. The correlation between variables x and y is

r

=

1 (n-1)sxsy

[(x1

-

?x)(y1

-

?y )

+

(x2

-

?x)(y2

-

?y )

+

...

+

(xn

-

?x)(yn

-

?y)] .

The least squares regression line is where

y = ax + b.

a=r

sy sx

and

b = ?y - a?x.

For a simple random sample of size n,

the sample proportion of successes is

p

=

count

of successes

n

in the

sample

The mean of the sampling distribution is p

and the standard deviation is

p(1-p) n

.

The 68 - 95 - 99.7 Rule applies here aswell.

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